Prove that (a+b)⋅(a+b)=∣a∣2+∣∣b∣∣2, if and only if a,bare perpendicular, given a=0,b=0
If a,b,c are non-coplanar vector and λ is a real number, then the vectors a+2b+3c,λb+μcand(2λ−1)c are coplanar when a. μ∈R b. λ=21 c. λ=0 d. no value of λ
If 4i^+7j^+8k^,2i^+3j^+24and2i^+5j^+7k^ are the position vectors of the vertices A,BandC, respectively, of triangle ABC , then the position vecrtor of the point where the bisector of angle A meets BC is a. 32(−6i^−8j^−k^) b. 32(6i^+8j^+6k^) c. 31(6i^+13j^+18k^) d. 31(5j^+12k^)
If a,bandc are three non-zero vectors, no two of which ar collinear, a+2b is collinear with c and b+3c is collinear with a, then find the value of ∣∣a+2b+6c∣∣˙
Sow that x1i^+y1j^+z1k^,x2i^+y2j^+z2k^,andx3i^+y3j^+z3k^, are non-coplanar if ∣x1∣>∣y1∣+∣z1∣,∣y2∣>∣x2∣+∣z2∣and∣z3∣>∣x3∣+∣y3∣ .
Given four points P1,P2,P3andP4 on the coordinate plane with origin O which satisfy the condition (OP)n−1+(OP)n+1=23OPn (i) If P1 and P2 lie on the curve xy=1 , then prove that P3 does not lie on the curve (ii) If P1,P2,P3 lie on a circle x2+y2=1, then prove that P4 also lies on this circle.
Given three points are A(−3,−2,0),B(3,−3,1)andC(5,0,2)˙ Then find a vector having the same direction as that of AB and magnitude equal to ∣∣AC∣∣˙